A martingale bound for the entropy associated with a trimmed filtration on <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mrow><mi mathvariant="italic">d</mi></mrow></msup></math>
Using martingale methods, we provide bounds for the entropy of a probability measure on ${\mathbb{R}}^{d}$ with the right-hand side given in a certain integral form. As a corollary, in the one-dimensional case, we obtain a weighted log-Sobolev inequality.
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
VTeX
2015-02-01
|
| Series: | Modern Stochastics: Theory and Applications |
| Subjects: | |
| Online Access: | https://vmsta.vtex.vmt/doi/10.15559/15-VMSTA16 |